Aumann and Serrano :810–836, 2008) introduce the axiom of duality, which ensures that risk measures respect comparative risk aversion. This paper characterizes all dual risk measures by a simple equivalent condition. This equivalence provides a decomposition result and a construction method, which is used to analyze concrete dual measures. Moreover, this paper aims to extend this characterization to the most general setting. Compared with Aumann and Serrano, it, therefore, relaxes the axiom of positive homogeneity, and allows for risk-neutral and risk-seeking (...) agents, as well as for all integrable gambles. (shrink)